5x^2-20x-65=0

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Solution for 5x^2-20x-65=0 equation: 


Simplifying
5x2 + -20x + -65 = 0

Reorder the terms:
-65 + -20x + 5x2 = 0

Solving
-65 + -20x + 5x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-13 + -4x + x2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-13 + -4x + x2)' equal to zero and attempt to solve:

Simplifying
-13 + -4x + x2 = 0

Solving
-13 + -4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '13' to each side of the equation.
-13 + -4x + 13 + x2 = 0 + 13

Reorder the terms:
-13 + 13 + -4x + x2 = 0 + 13

Combine like terms: -13 + 13 = 0
0 + -4x + x2 = 0 + 13
-4x + x2 = 0 + 13

Combine like terms: 0 + 13 = 13
-4x + x2 = 13

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = 13 + 4

Reorder the terms:
4 + -4x + x2 = 13 + 4

Combine like terms: 13 + 4 = 17
4 + -4x + x2 = 17

Factor a perfect square on the left side:
(x + -2)(x + -2) = 17

Calculate the square root of the right side: 4.123105626

Break this problem into two subproblems by setting 
(x + -2) equal to 4.123105626 and -4.123105626.


Subproblem 1
x + -2 = 4.123105626

Simplifying
x + -2 = 4.123105626

Reorder the terms:
-2 + x = 4.123105626

Solving
-2 + x = 4.123105626

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '2' to each side of the equation.
-2 + 2 + x = 4.123105626 + 2

Combine like terms: -2 + 2 = 0
0 + x = 4.123105626 + 2
x = 4.123105626 + 2

Combine like terms: 4.123105626 + 2 = 6.123105626
x = 6.123105626

Simplifying
x = 6.123105626


Subproblem 2
x + -2 = -4.123105626

Simplifying
x + -2 = -4.123105626

Reorder the terms:
-2 + x = -4.123105626

Solving
-2 + x = -4.123105626

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '2' to each side of the equation.
-2 + 2 + x = -4.123105626 + 2

Combine like terms: -2 + 2 = 0
0 + x = -4.123105626 + 2
x = -4.123105626 + 2

Combine like terms: -4.123105626 + 2 = -2.123105626
x = -2.123105626

Simplifying
x = -2.123105626


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.123105626, -2.123105626}
Solution
x = {6.123105626, -2.123105626}

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